From rbotting@wiley.csusb.edu Tue Feb 15 10:49 PST 1994 Return-Path: Received: from wiley.csusb.edu by silicon.csci.csusb.edu (5.0/SMI-SVR4) id AA16403; Tue, 15 Feb 94 10:49:35 PST Received: by wiley.csusb.edu (5.67a/1.34) id AA11964; Tue, 15 Feb 1994 10:50:46 -0800 Date: Tue, 15 Feb 1994 10:50:46 -0800 From: rbotting@wiley.csusb.edu ("Dr. Richard Botting") Message-Id: <199402151850.AA11964@wiley.csusb.edu> To: dick@silicon.csci.csusb.edu Subject: (fwd) Re: Finding minimums of a set Newsgroups: comp.specification.z Content-Type: text Content-Length: 2356 Status: R Newsgroups: comp.specification.z Path: csus.edu!wupost!howland.reston.ans.net!usenet.ins.cwru.edu!news.ecn.bgu.edu!siemens!ps From: ps@scr.siemens.com (Phil Stocks) Subject: Re: Finding minimums of a set Message-ID: Sender: news@scr.siemens.com (NeTnEwS) Nntp-Posting-Host: kingswood.siemens.com Organization: Siemens Corporate Research, Princeton (Plainsboro), NJ References: <2jnljp$6lt@greene.dur.ac.uk> Date: Mon, 14 Feb 1994 14:31:52 GMT Lines: 39 Alexis Manning writes: >I have a partial function from a given set to a natural number. What I'm >after doing is to find which member(s) of the given set map to the lowest >natural number. I thought that there was some sort of \min function, but If I understand what you're trying to achieve, this passes fUZZ for me: \begin{zed} [GIVEN] \end{zed} \begin{axdef} f: GIVEN \pfun \nat \end{axdef} \begin{axdef} m: \power GIVEN \where m = f\inv \limg \{min (\ran f)\} \rimg \end{axdef} Is that what you're after? The variable m here is a set, because there could be more than one member of GIVEN which maps to the minimum range element of f. You can use various methods (\mu, \exists) to get an arbitrary element of m. >While I'm on, can anyone recommend a good fuzz reference? My Z textbook >is damnably useful, but not particularly helpful in isolating which fuzz >command is required. (Or in helping with fuzz's error messages) There is a fUZZ manual (called "The fUZZ Manual", oddly enough) by Mike Spivey. I thought it came with fUZZ. I haven't wanted to do anything with fUZZ that I couldn't find out how to do in some form from the manual. --------------------------------------------------------------------------- Phil Stocks ps@scr.siemens.com Siemens Corporate Research, Inc. tel: +1 609 734 3649 755 College Road East, Princeton, NJ 08540 fax: +1 609 734 6565 -- rbotting@wiley.csusb.edu. rbotting::=`Dr. Richard J. Botting`, wiley::=`Faculty EMail System`, csusb::=`California State University, San Bernardino, CA 92407, USA`. Aka::=`dick@doc.csci.csusb.edu`. Disclaimer::=`CSUSB may or may not agree with this message`. Copyright(1994)::=`Copy and use as you wish as long as you include this copywrite and signature`. From rbotting@wiley.csusb.edu Thu May 19 11:59 PDT 1994 Return-Path: Received: from wiley.csusb.edu by silicon.csci.csusb.edu (5.0/SMI-SVR4) id AA27643; Thu, 19 May 94 11:59:08 PDT Received: by wiley.csusb.edu (5.67a/1.34) id AA14066; Thu, 19 May 1994 11:59:08 -0700 Date: Thu, 19 May 1994 11:59:08 -0700 From: rbotting@wiley.csusb.edu ("Dr. Richard Botting") Message-Id: <199405191859.AA14066@wiley.csusb.edu> To: dick@silicon.csci.csusb.edu Subject: (fwd) Re: A question about style (or a problem with Z?) Newsgroups: comp.specification.z Content-Type: text Content-Length: 2468 Status: R Path: csus.edu!wupost!howland.reston.ans.net!spool.mu.edu!news.clark.edu!netnews.nwnet.net!news.u.washington.edu!news.u.washington.edu!jon From: jon@bilbo.radonc.washington.edu (Jon Jacky) Newsgroups: comp.specification.z Subject: Re: A question about style (or a problem with Z?) Date: 13 May 94 15:44:52 Organization: /users/jon/.organization Lines: 48 Distribution: world Message-ID: References: <2qgc0c$8i9@cybernet.cse.fau.edu> <2qkg0s$apn@uqcspe.cs.uq.oz.au> NNTP-Posting-Host: bilbo.radonc.washington.edu In-reply-to: brendan@cs.uq.oz.au's message of 9 May 1994 05:00:12 GMT I'm a bit puzzled by this thread. Everyone realizes you can update a function at one value (leaving the rest unchanged) using the override operator, f' = f (+) { k |-> d } but some of the discussion suggests that updating a function at more than one value is a special problem that requires a rather complicated solution. The override operator works just as well at multiple values: f' = f (+) { k1 |-> d1, k2 |-> d2, k3 |-> d3 } So you don't need to define different operations for updating with one, two and more values. This works for any number of values: F == Key -+> Data +--Update--------------- | f, f': F | updates?: F +---------------------- | f' = f (+) updates? +---------------------- You can specialize this if you must have names for updates with particular numbers of values: +--DoubleUpdate--------- | Update | k1?,k2?: Key | d1?,d2?: Data +----------------------- | updates? = { k1? |-> d1?, k2? |-> d2? } +----------------------- The definition of overriding ensures that the function remains the same at values outside the domain of ``updates?'' - Jon -- Jonathan Jacky jon@radonc.washington.edu Radiation Oncology RC-08 voice: (206)-548-4117 University of Washington FAX: (206)-548-6218 Seattle, Washington 98195 USA -- rbotting@wiley.csusb.edu. rbotting::=`Dr. Richard J. Botting`, wiley::=`Faculty EMail System`, csusb::=`California State University, San Bernardino, CA 92407, USA`. Aka::=`dick@doc.csci.csusb.edu`. Disclaimer::=`CSUSB may or may not agree with this message`. Copyright(1994)::=`Copy and use as you wish as long as you include this copyright and signature`. Send EMail to gradinfo@silicon.csci.csusb.edu for info on a new Masters degree in Computer Science!